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Effects of Marangoni Convection on the Mass Transfer Performance in a Packed-Bed Absorber Honda Wu,† Tsair-Wang Chung,*,† and Ming-Hong Lai‡ Chemical Engineering Department, Chung-Yuan University, Chungli, 32023 Taiwan, Republic of China
The process of absorbing water vapor into triethylene glycol (TEG) solutions is achieved in two steps. In the first step, water vapor is condensed into water droplets on the gas-liquid interface. The second step involves the dissolution of water droplets into the TEG solution as a result of the change in surface tension in the surface thin film. This study is focused on the effects of the surface tension gradient on mass transfer performance of the absorption process. An investigation of the disturbance induced by the surface tension gradient and an evaluation of the mass transfer behavior were conducted. As noted, the phenomenon of fluid flow in the surface thin film due to the surface tension gradient is termed the Marangoni effect, and the induced convection is usually termed Marangoni convection. To discuss the relationship between the Marangoni effect and the mass transfer performance, the surface tension of the liquid desiccant was measured under different temperatures and concentrations during experimental runs. The conventional mass transfer correlation was modified by using the term of the M index, which combines the surface tension gradient and the driving force of mass transfer to explain Marangoni effects. This improves the average error between predicted values and experimental data significantly. Introduction Zarzycki and Chacuk1 found that surface flow was induced by the surface tension gradient in wetted-wall, packed-bed, and plate columns. On the basis of their descriptions, the Marangoni effect resulting from surface tension gradient was found to affect the mass transfer performance in those typical absorption columns. As noted by them, one of the most significant physicochemical properties of the working solution related to the mass transfer mechanism could be the surface tension. The conventional mass transfer theories, such as film theory, penetration theory, and surface renewal theory, did not consider the effects of the surface tension on the mass transfer performance. Although the boundary layer theory incorporated the concept of a hydraulic boundary layer, it still did not clearly identify the effect of this physicochemical property on the mass transfer performance. Discussions of conventional gas-liquid contacting devices on the basis of their mass transfer performance incorporated with Marangoni effects were limited. There are some investigators studying the Marangoni effect in distillation processes. However, similar studies on packed absorbers are rare so far. Zuiderweg and Harmens2 demonstrated that the distillation efficiency of a bubble tower with a continuous liquid phase is higher than that of a spray tower with a dispersive liquid phase at the same operating conditions because the Marangoni effect occurred in the bubble tower. Furthermore, Patberg et al.3 found that * To whom correspondence should be addressed. Dr. TsairWang Chung, Associate Professor, Department of Chemical Engineering, Chung-Yuan University, Chungli 32023, Taiwan, ROC. Fax: 886-3-4563171 ext 4199. Phone: 886-3-4563171 ext 4125. E-mail:
[email protected]. † Chung-Yuan University. ‡ Present address: Taiwan Police College, Taipei, Taiwan, ROC.
the transfer of a component with lower surface tension from the liquid to the gas phase results in an increase in the surface tension of the remaining liquid, which is termed the Marangoni positive, so that the packing materials can be completely wetted by the liquid. On the other hand, while the component evaporates with relatively higher surface tension, the remaining liquid can form spots, which is termed the Marangoni negative, and as a consequence, the channeling phenomenon can occur in the packed bed. Because the surface tension gradient increased the disturbance in the surface thin film, Smigelschi et al.4 and Ruckenstein et al.5 tried to add the surfactant isobutanol to the air-water interface to enhance the efficiency of absorbing CO2 from air. They also adopted the convection-diffusion equation to discuss the velocity contribution of the surface flow and showed that the derivation was consistent with experiment. In addition, the local surface tension gradient resulting from the temperature difference of vaporizing the fluid layer at the gas-liquid interface is called an instability. Berg and Acrivos6 found that, when a surfactant with lower surface tension was added to the liquid surface, it would stabilize the fluid flow at the surface. The studies related to the Marangoni effect on fluid flow in surface thin films and on the distillation column performance are shown in Table 1. A discussion of the disturbance induced by the surface tension gradient on mass transfer performance in a packed-bed absorber is presented in this study. To make the liquid flow in a continuous phase and avoid channeling effects in the packed column, the liquid flow rates were operated beyond the minimum liquid flow rate. In general, the process variables of the packed-bed absorption systems include the gas and liquid flow rates, gas and liquid temperatures, concentrations of liquid desiccant solutions, and type and size of the packings. The mass transfer performance of the packed-bed absorber in this study is discussed in terms of the process
10.1021/ie000468a CCC: $20.00 © 2001 American Chemical Society Published on Web 01/09/2001
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Table 1. Some Studies Related to the Marangoni Effect in the Literature discussion of the gas-liquid interfacial phenomenon during the absorption process discussion of the Marangoni effect on distillation column performance comparison of distillers with and without the Marangoni effect
Smigolischi et al.4 Lu et al.13 Lu et al.14 Vazquez et al.18 Wu et al.19 Zuiderweg and Harmens2 Patberg et al.3 Zuiderweg16 Billet and Schultes20 Proctor et al.21 Zuiderweg and Harmens2 Patberg et al.3 Moens and Bos22 Semkov and Kolev23
Table 2. Some Studies of Mass Transfer Performance in the Literature Chung et al.10 Ullah et al.24 Chung et al.25 Sadasivan and Balakrishnan26 discussion of the mass Gandhidasan et al.9 transfer coefficient Chung et al.10 Chung et al.25 Sadasivan and Balakrishnan26 derivation and Gandhidasan et al.9 regression of the mass Chung et al.10 transfer correlation Aroonwilas and Tontiwachwuthikul11 Onda et al.17 Nielsen et al.27 discussion of the column or removal efficiency
Figure 1. Liquid desiccant dehumidifier of this study.
variables mentioned above. Discussions of mass transfer performance are usually categorized into three portions, including the column efficiency, the mass transfer coefficient, and the derivation and regression of the mass transfer correlation (shown in Table 2). Discussions of the Marangoni effect in packed-bed absorption systems are limited in the open literature. However, these discussions help us understand the mechanisms of water molecules dissolved in the liquid desiccant solution and more information can be acquired, such as the mass transfer mechanisms of the packed-bed absorption system, improvement of the column efficiency, and reduction of the discrepancy in the correlation. Experimental Section Experiments were conducted in an absorption-stripping system. The configuration and the structure of the absorber are shown in Figure 1. The design of an inverse U-shaped air tunnel with an eliminator in the absorber allow for countercurrent contact between the air and the solution, which reduces carryover of the solution.
Figure 2. Water vapor condenses into water droplets.
In this absorption system, liquid desiccant solutions flow into the absorber through nozzles and leave from the bottom of the absorber. Three full-cone nozzles were used as the liquid distributor, and 2-in. polypropylene Flexi rings were packed in the absorber. The solution flow rates were determined by calculations of the minimum wetting rate.7 Because the solution flow rates selected in this study are much larger than the minimum wetting rate and because the mass transfer is occurred in the gas-liquid interface, whose area is more than 3 m2 in this packed tower, end effects are negligible. The air inlet and outlet are on both sides of the absorber. The setup of the stripper is similar to that of the absorber. This system can vary the air flow rates from 0.047 to 0.063 kg/s and the liquid flow rates from 0.17 to 0.26 kg/s. The surface tensions of the TEG solutions were measured by a surface tension meter (CBVP A-3). The mass transfer coefficients were calculated from the absorption of water vapor by the TEG solutions. The concentrations of the TEG solutions were measured by a refractometer. A testo-400 hygrometer with two humidity probes was used to measure the absolute and relative humidity and temperature of the air. The air flow rates were controlled by transistor inverters on the 1 HP blowers. The liquid flow rates were controlled by rotameters and global valves, and the air velocities were measured with a hot-wire flow meter. Discussions of the relationship between the mass transfer performance and the disturbance resulting from the surface tension gradient are the purpose of this study. A continuous and uniform fluid on the packing surface was maintained, and channeling effects were avoided. When the surface tension gradient resulting from absorbing water vapor is large enough to exhibit the Marangoni effect, the disturbance in the surface thin film takes place. Furthermore, the surface tension of the liquid desiccant solution varies with the concentration and temperature of the solution. Therefore, the experiments in this study were conducted by means of variations in the air and liquid flow rates as well as the concentrations and temperatures of the TEG solution. Formula Derivation In the process of the absorption of water vapor by the TEG solutions, water vapor is condensed to water droplets on the liquid surface. Because the density of the TEG solution is larger than that of water droplets, the shape of the water droplets becomes a circular sheet over the solution surface, as shown in Figure 2. Because of the surface tension gradient induced by the leading edge of the circular sheet and the TEG solution, the disturbance of a surface thin film causes a nonuniform surface stress. The larger the surface tension gradient,
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 887
kxa )
yAin - yAi L ln V yAout - yAi
(7)
From Dalton’s partial pressure law
PyA ) PA
(8)
the mole fraction yA in eq 7 can be represented by the ratio of the partial pressure and the total pressure, i.e.
PAin PAi L P P kxa ) ln V PAout PAi P P
Figure 3. (a) Continuous fluid flow in the packed-bed column and (b) fluid flow on a packing surface (scale-up).
the more intensive the disturbance of the thin film that occurs. A schematic diagram of a packed-bed absorber is shown in Figure 3a. The continuous liquid film on the packing surface, as shown in Figure 3b, is assumed to be a stagnant film. The mass balance can be written as
NA dA ) kx(xAi - xA)a dV ) L dxA ) G dyA
(1)
where kx is the mass transfer coefficient of diffusing water vapor into the stagnant film of TEG solution on the packing surface. Compared to the mass transfer coefficient, kx′, in the different case of equimolar counterdiffusion, kx is equal to kx′ divided by a (1 - xA)lm term corresponding to a bulk flow concentration factor for transfer through a stagnant film (Geankoplis,8 1993). For dilute systems, the log-mean term approaches 1, and kx is similar to kx′. L and G are the molar flow rates of liquid and gas, respectively. By considering mass transfer in the liquid phase, eq 1 becomes
kxa(xAi - xA) dV ) L dxA
(2)
where kxa represents the volumetric mass transfer coefficient. Therefore, eq 2 becomes
kxa(xAi - xA) dV ) L dxA
(3)
Integration of eq 3 with respect to the packed-bed volume and the concentration of water molecules yields
L xAout dxA kxa ) V xAin xAi - xA
∫
(4)
The concentration of water molecule at the gas-liquid interface can be assumed to be a constant in the equilibrium state during absorption process. Let mole fraction of xAi be a constant. Equation 4 is integrated and rewritten as
kxa )
xAi - xAin L ln V xAi - xAout
ky (y - yAi) kx A
Substituting eq 6 into eq 5, we find
Because water molecules are very soluble in the TEG solution, the process of dehumidification is regarded as a gas-phase-resistance-controlling system, i.e.
1 1 . ky kx
(10)
yA - yAi . xAi - xA
(11)
and
In a gas-liquid contact system, the concentration profile is represented as in Figure 4. Because water molecules are very soluble in the TEG solution, once the water vapor touches the TEG solution surface, the water vapor is changed to the liquid phase right away. Therefore, the inequality PA/P . PAi/P holds, and PAi approaches 0 at the interface. Thus, eq 9 is simplified to the following formula:
PAin P L kxa ) ln V PAout P
(12)
From Chapter 9 of the book by Geankoplis,8 the partial pressure of water vapor in air can be represented by the humidity of the air.
PA 28.97 × H ) P 18.02 + 28.97H
(13)
The term PA/P in eq 12 is replaced by eq 13. Equation 12 then becomes
28.97Hin 18.02 + 28.97Hin L kxa ) ln V 28.97Hout 18.02 + 28.97Hout
(14)
(5)
As noted, the molar fluxes in the gas and liquid films are the same and ky(yA - yAi) is equal to kx(xAi - xA). Therefore
xAi - xA )
(9)
(6)
The above equation was used to estimate the mass transfer coefficients in this study. Results and Discussions 1. Discussion of kx and kxa. Because the mass transfer performance of the absorber is affected by the gas-liquid contacting area, it is reasonable to use the values of kxa9-11 to assess the performance of the
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Figure 4. Gas- and liquid-phase concentration gradients at the gas-liquid interface.
Figure 6. Effect of air flow rate on liquid-phase mass transfer coefficient.
Figure 5. Effect of liquid flow rate on liquid-phase mass transfer coefficient.
absorber. However, to calculate the Marangoni number,12 Ma ) σi - σB/(µLk*x), estimations of k12-15 are also necessary. The M index is a popular index used to describe the Marangoni effect. Not only the rate change of surface tension, but also the driving force for mass transfer, is taken into account through adoption of the M index. Therefore, the M index was used to discuss the effects of surface tension on the mass transfer performance in this study. 2. kxa Influenced by Process Variables. On the basis of the disturbance resulting from the surface tension gradient, the different temperatures and concentrations of the liquid were controlled and the gas and liquid flow rates were fixed at the same operating condition for studying the effect of the disturbance level on the mass transfer coefficients. However, the conventional interpretations were usually used to explain the effect of the gas and liquid flow rates on kxa. As shown in Figure 5, when the air flow rate is kept constant, the value of kxa increases as the liquid flow rate increases. Because the amount of treated air is fixed and the amount of absorbent (TEG) is increased, the mass transfer coefficients should increase. However, Figure 6 shows that the mass transfer coefficient decreases with an air flow rate increase when the liquid flow rate is kept constant. Similarly, when the amount of treated air is increased and the amount of absorbent (TEG) is fixed, the value of the mass transfer coefficient should decrease. When the air and liquid flow rates are kept constant, the mass transfer performance in Figure 7 increases as the inlet humidity increases. On the basis of the concept
Figure 7. Effect of air inlet humidity on liquid-phase mass transfer coefficient.
of the disturbance induced by the surface tension gradient, this result can be clearly explained. The definition of each local position of water vapor absorbed by TEG solution is termed an absorption site in this study. The number of absorption sites increases as the air humidity increases, thereby increasing the disturbance area. Therefore, the value of kxa is increased by increasing the air humidity. In addition, studies of the effects on the liquid-phase mass transfer coefficient of variations in the temperature and concentration of the liquid desiccant solution were also conducted by other researchers. Because the surface tension of the liquid desiccant solution is a function of the temperature and concentration, the parameters of temperature and concentration of liquid desiccant solution were replaced by surface tension to discuss the mass transfer coefficient for the liquid phase. Not only the relationship between the mass transfer performance and the surface tension gradient but also the changes in the surface tension of the TEG solution due to different temperatures and concentrations were acquired in this study. As shown in Table 3, the surface tension of the triethylene glycol solutions increases as
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 889 Table 3. Surface Tension of Triethylene Glycol Solution at Different Concentrations and Temperatures TEG conc (wt %)
TEG temp (°C)
surface tension (dyne/cm)
99.96 99.96 99.96 99.96
35 30 25 20
44.5 44.7 45.0 45.4
97.60 97.60 97.60 97.60 97.60
35 30 25 20 15
44.8 45.1 45.3 45.7 46.1
94.50 94.50 94.50 94.50 94.50
35 30 25 20 15
45.3 45.5 45.8 46.2 46.6
93.00 93.00 93.00 93.00 93.00
35 30 25 20 15
45.5 45.7 45.9 46.3 46.8
90.00 90.00 90.00 90.00 90.00
35 30 25 20 15
45.9 46.1 46.4 46.8 47.2
88.00 88.00 88.00 88.00 88.00
35 30 25 20 15
46.2 46.5 46.8 47.1 47.5
Figure 8. Relationship between concentration of desiccant solution and the ratio of the surface tensions of the TEG solution and water.
the temperature decreases and decreases as the concentration increases. The values of the M index16 in this study of the Marangoni effect are calculated via
M ) ∆x
dσ′ dσ′ ) (x - x*) dx dx
(15)
where ∆x represents the driving force for mass transfer and dσ′/dx is the change in the dimensionless surface tension with mole fraction. The dimensionless surface tension is defined as
σ′ ) σsoln/σH2O
(16)
As shown in Figure 8, the change in the surface tension increased with increasing mole fraction of water. Because the M index is the combination of the surface tension gradient and the driving force, the relationship between these two variables is not linear. The larger the value of the M index, the more intensive the surface disturbance. Therefore, it can be seen from Figure 10 that kxa increases with increasing M index. 3. Mass Transfer Correlation Incorporated with Surface Tension Difference. The mass transfer coefficients calculated from eq 14 were correlated in terms of the process variables by employing a dimensional analysis. Variables that affect the mass transfer coefficient for the liquid phase include the air and liquid flow rates, the physical properties of the air and liquid, the packing volume and size, and the diffusion coefficient of water in the TEG solution. In functional form, the mass transfer coefficient can be expressed as
f(kxa, DL, dp, dc, FL, G, L, µL, M) ) 0
(17)
Figure 9. Comparison between experimental and predicted mass transfer coefficients using the correlation without the M index term.
The above variables are arranged into pertinent dimensionless groups by using the Buckinghan pi method. The mass transfer correlation obtained from the dimensional analysis is given below as
( )( ) ( )
kxaMdp2 FLLdp )b µL µL
c
µL DL F L
d
e
L G
(18)
where b, c, d, and e are constants that are obtained by a nonlinear regression of the experimental data. The experimental data of this study were used to evaluate the constants in eq 16. The correlation was obtained as
( )( )()
FLLdp kxaMdp2 ) 1 × 10-7 µL µL
0.5
µL DLFL
1/3
L G
0.81
(19)
The above correlation was applied to predict the mass transfer coefficients under different temperatures and concentrations in the experimental runs. The average error was 15%, as shown in Figure 9. As mentioned
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enhances the mass transfer coefficient but also practically affects the mass transfer mechanism. Conclusion
Figure 10. Effect of the M index on the liquid-phase mass transfer coefficient.
Generally speaking, discussions of the effects of process variables on absorption processes sometimes neglect the physical properties of the working solutions, such as their surface tension. However, the surface tension affects the mass transfer mechanism significantly. The surface traction resulting from the surface tension gradient of absorbing water vapor into a TEG solution is one of the most important reasons causing the disturbance phenomenon in the surface thin film. The concept of a surface fluid disturbance induced by the surface tension gradient was suggested in this paper. Through a consideration of the disturbance occurring in surface thin film, the mass transfer performance in the air dehumidification process can be explained successfully. The mass transfer correlation obtained by using dimensional analysis, which involves the ratio of the liquid and gas flow rates and the M index, reduces the average error between the predicted values and the experimental data to about 7%. Furthermore, to understand the mass transfer mechanism exactly, additional studies related to surface flow will be conducted in the future. Acknowledgment This work is supported by the National Science Council of the Republic of China under Grant NSC882214-E-033-004. Nomenclature
Figure 11. Comparison between experimental and predicted mass transfer coefficients using the correlation with the M index term.
earlier, the M index is a key variable affecting the mass transfer coefficient, as shown in Figure 10. The M index should be taken into account in the mass transfer correlation. The mass transfer correlation obtained by using the dimensional analysis and nonlinear regression is given as
( )( )()
kxaMdp2 FLLdp ) 1 × 10-7 µL µL
0.5
µL DLFL
1/3
L G
1.55
M0.25 (20)
This mass transfer correlation is different from that of Onda et al.17 The ratios of liquid to air flow rate and M index, which involve physical properties of the liquid desiccant solution, were considered in this correlation to reduce the average error. The values of the mass transfer coefficient calculated from eq 14 and predicted from eq 18 were plotted in Figure 11. About 90% of the data points are within the (15% error, and the average error was 7%. The results demonstrate that the disturbance induced by the surface tension gradient not only
a ) surface area of liquid film per unit volume of packed bed, m2/m3 D ) diffusion coefficient, m2/s dc ) column diameter, m dp ) packing diameter, m G ) gas flow rate, kmol/s H ) humidity, kg of H2O/kg of dry air kx ) mass transfer coefficient in the case of diffusion to a stagnant film, kmol m-2 s-1 (mole fraction) kx′ ) mass transfer coefficient in the case of equimolar counterdiffusion, kmol m-2 s-1 (mole fraction) ky ) mass transfer coefficient in the case of equimolar counterdiffusion for the gas phase, kmol m-2 s-1 (mole fraction) L ) liquid flow rate, kmol/s M ) molecular weight of air, kg/kmol P ) total pressure, mmHg PA ) partial pressure of H2O, mmHg T ) liquid temperature, °C V ) packing volume, m3 (1 - xA)lm ) bulk flow concentration factor, [(1 - xA) (1 - xAi)]/ln[(1 - xA)/(1 - xAi)] xA ) mole fraction of H2O in TEG solution, mol/mol xA* ) xA in equilibrium with yA yA ) mole fraction of H2O in gas phase, mol/mol µL ) liquid viscosity, kg m/s FL ) liquid density, kg/m3 σ′ ) dimensionless surface tension, σsoln/σH2O σsoln ) surface tension of solution, N/m σH2O ) surface tension of water molecules, N/m Subscripts A ) H2O component x ) liquid phase
Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001 891 y ) gas phase L ) liquid G ) gas i ) interface B ) bulk solution
Literature Cited (1) Zarzycki, R.; Chauck, A. Absorption Fundamentals & Applications; Pergamon Press: New York, 1993. (2) Zuiderweg, F. J.; Harmens, A. The influence of surface phenomena on the performance of distillation columns. Chem. Eng. Sci. 1958, 9, 89-108. (3) Patberg, W. B.; Koers, A.; Steenge, W. D. E.; Drinkeburg, A. A. H. Effectiveness of mass transfer in a packed distillation column in relation to surface tension gradients. Chem. Eng. Sci. 1983, 38 (6), 917-923. (4) Smigelschi, O.; Suciu, D. G.; Ruckenstein, E. Absorption under the action of artificially provoked Marangoni effect. Chem. Eng. Sci. 1969, 24, 1227-1234. (5) Ruckenstein, E.; Smigelschi, O.; Suciu, D. G. A steady dissolving drop method for studying the pure Marangoni effect. Chem. Eng. Sci. 1970, 25, 1249-1254. (6) Berg, J. C.; Acrivos, A. The effect of surface active agents on convection cells induced by surface tension. Chem. Eng. Sci. 1965, 20, 737-745. (7) Sawistowski, H.; Smith, W. Mass Transfer Process Calculation; Imperial College of Science and Technology: London, 1963. (8) Geankoplis, C. J. Transport Processes and Unit Operations; Prentice Hall: Englewood Cliffs, NJ, 1993. (9) Gandhidasan P.; Kettleborough, C. F.; Ullah, M. R. Calculation of heat and mass transfer coefficients in a packed tower operating with a desiccant-air contact system. J. Sol. Energy Eng. 1986, 108, 123-128. (10) Chung, T. W.; Ghosh, T. K.; Hines, A. L. Comparison between random and structured packings for dehumidification of air by lithium chloride solutions in a packed column and their heat and mass transfer correlations. Ind. Eng. Chem. Res. 1996, 35, 192-198. (11) Aroonwilas, A.; Tontiwachwuthikul, P. Mass transfer coefficients and correlation for CO2 absorption into 2-amino-2methyl-1-propanol (AMP) using structured packing. Ind. Eng. Chem. Res. 1998, 37, 569-575. (12) Brian, P. L. T.; Vivian, J. E.; Mayr, S. T.; Cellular convection in desorbing surface tension-lowering solutes from water. Ind. Eng. Chem. Fundam. 1971, 10 (1), 75. (13) Lu, H. H.; Yang, Y. M.; Maa, J. R. Effect of artificially provoked Marangoni convection at a gas/liquid interface on absorption. Ind. Eng. Chem. Res. 1996, 35, 1921-1928. (14) Lu, H. H.; Yang, Y. M.; Maa, J. R. On the induction criterion of the Marangoni convection at the gas/liquid interface. Ind. Eng. Chem. Res. 1997, 36, 474-482.
(15) Fujinawa, K.; Hozawa, M.; Imaishi, N. Effects of desorption and absorption of surface tension-lowering solutes on liquid-phase mass transfer coefficients at a turbulent gas-liquid interface. J. Chem. Eng. Jpn. 1978, 11 (2), 107-111. (16) Zuiderweg, F. J. Marangoni effect in distillation of alcoholwater mixtures. Chem. Eng. Res. Des. 1983, 61, 388-390. (17) Onda, K.; Takeuchi H.; Okumoto, Y. Mass transfer coefficients between gas and liquid phases in packed columns. J. Chem. Eng. Jpn. 1968, 1 (1), 56-62. (18) Vazquez, G.; Antorrena, G.; Navaza, J. M.; Santos, V. Absorption of CO2 by water and surfactant solutions in the presence of induced Marangoni effect. Int. Chem. Eng. 1994, 34 (2), 247-254. (19) Wu, T. C.; Lu, H. H.; Yang, Y. M.; Maa, J. R. Absorption Enhancement by the Marangoni effect - pool absorption of steam by aqueous lithium bromide solutions. J. Chin. Inst. Chem. Eng. 1994, 25 (5). (20) Billet, R.; Schultes, M. Predicted mass transfer in packed columns. Chem. Eng. Technol. 1993, 16, 1-9. (21) Proctor, S. J.; Biddulph, M. W.; Krishnamurthy, K. R. Effect of Marangoni surface tension forces on modern distillation packings. AIChE J. 1998, 44 (4), 831-835. (22) Moens, F. P.; Bos, R. G. Surface renewal effects in distillation. Chem. Eng. Sci. 1972, 27, 403-408. (23) Semkov, KR.; Kolev, N. On the evaluation of the interfacial turbulence (the Marangoni effect) in gas (vapor)-liquid mass transfer: Part I. A method for estimating the interfacial turbulence effect. Chem. Eng. Process. 1991, 29, 77-82. (24) Ullah, M. R.; Kettleborough, C. F.; Gandhidasan, P.; Effectiveness of moisture removal for an adiabatic counterflow packed tower absorber operating with CaCl2-air contact system. Trans. ASME 1988, 110, 98-101. (25) Chung, T. W.; Ghosh, T. K.; Hines, A. L. Dehumidification of moist air with simultaneous removal of selected indoor pollutants by triethylene glycol solutions in a packed-bed absorber. Sep. Sci.Technol. 1995, 30, 1807-1832. (26) Sadasivan, M.; Balakrishnan, A. R. Experimental investigations on the thermal effects in packed-bed liquid desiccant dehumidifiers. Ind. Eng. Chem. Res. 1994, 33, 1636-1640. (27) Nielsen, C. H. E.; Kiil, S.; Thomsen, H. W.; Dam-Johansen, K. Mass transfer in wetted-wall columns: correlations at high Reynolds numbers. Chem. Eng. Sci. 1998, 53 (3), 495-503. (28) Hines, A. L.; Maddox, R. N. Mass Transfer Fundamentals and Applications; Prentice Hall: Englewood Cliffs, NJ, 1985; Chapter 5.
Received for review May 5, 2000 Revised manuscript received October 18, 2000 Accepted November 8, 2000 IE000468A
